{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "## load pacakges\n",
    "push!(LOAD_PATH, pwd()) # add the current folder, which contains Utils.jl, to LOAD_PATH\n",
    "using Utils, DataFrames, PyPlot, NLsolve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "## matplotlib settings\n",
    "#  not important, only to write latex on graphs\n",
    "fontsize = 16; fonttype = \"serif\"\n",
    "# fonttype = \"sansserif\"\n",
    "PyPlot.matplotlib.rc(\"text\", usetex=true) # allow tex rendering\n",
    "PyPlot.matplotlib.rcParams[\"text.latex.unicode\"] = true\n",
    "if fonttype==\"serif\" # use serif math font\n",
    "    PyPlot.matplotlib.rc(\"font\", family=\"serif\", serif=\"Times\", size=16)\n",
    "    #PyPlot.matplotlib.rc(\"text.latex\",preamble=\"\\\\usepackage[libertine]{newtxmath}\")\n",
    "else # use sans serif math font\n",
    "    PyPlot.matplotlib.rc(\"font\", family=\"sans-serif\", size=16)\n",
    "    PyPlot.matplotlib.rc(\"text.latex\",preamble=\"\\\\usepackage{newtxsf}\")\n",
    "end\n",
    "PyPlot.matplotlib.rcParams[\"text.latex.unicode\"] = false;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Functions to solve equilibrium"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matching (generic function with 1 method)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## general matching function\n",
    "function matching(searchingIntensity,matchingProb)\n",
    "    return searchingIntensity*matchingProb\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "solveDemographics (generic function with 1 method)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## solve for demographics\n",
    "function solveDemographics(para;guess=nothing)\n",
    "    ρ, n, λu, λd, yh, yd, yl, r, qLO, qHN, md, s, ψ = para\n",
    "    η = λu/(λu + λd)\n",
    "    function pi(μ) # the special π(.) as in Equation 1 in the paper\n",
    "        return ψ*μ/(ψ*μ + (1.0 - ψ)*(1.0 - μ))\n",
    "    end\n",
    "    function resolveDemographicsX(x)\n",
    "        di = Dict()\n",
    "        di[:mDO] = transBetween(x[1],lower=0.0,upper=md)\n",
    "        di[:mHN] = transBetween(x[2],lower=0.0,upper=η)\n",
    "        di[:mLO] = transBetween(x[3],lower=0.0,upper=1.0-η)\n",
    "        di[:mDN] = md - di[:mDO]\n",
    "        di[:mHO] = η - di[:mHN]\n",
    "        di[:mLN] = 1.0 - η - di[:mLO]\n",
    "        di[:νLO] = 1.0 - (1.0 - pi(di[:mDN]/md))^n\n",
    "        di[:νHN] = 1.0 - (1.0 - pi(di[:mDO]/md))^n\n",
    "        di[:vlm] = ρ*di[:mHN]*di[:νHN]\n",
    "        return di\n",
    "    end\n",
    "    function f!(fvec,x)\n",
    "        di = resolveDemographicsX(x)\n",
    "        fvec[1] = di[:mHO] + di[:mLO] + di[:mDO] - s\n",
    "        fvec[2] = di[:vlm] - ρ*di[:mLO]*di[:νLO]\n",
    "        fvec[3] = di[:mLO] - ((s - di[:mDO])*λd - di[:vlm])/(λd + λu)\n",
    "    end\n",
    "    if isnothing(guess)\n",
    "        guess = rand(3)\n",
    "    else\n",
    "        guess = [\n",
    "            transBetween(guess[1],lower=0.0,upper=md,reverse=true),\n",
    "            transBetween(guess[2],lower=0.0,upper=η,reverse=true),\n",
    "            transBetween(guess[3],lower=0.0,upper=1.0-η,reverse=true),\n",
    "        ]\n",
    "    end\n",
    "    sol = nlsolve(f!,guess)#,method=:newton)\n",
    "    converging = sol.x_converged | sol.f_converged\n",
    "    return converging, resolveDemographicsX(sol.zero)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "solveValueFunctions (generic function with 1 method)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## solve for value functions given demographics for a market\n",
    "function solveValueFunctions(para,di0)\n",
    "    ρ, n, λu, λd, yh, yd, yl, r, qLO, qHN, md, s, ψ = para\n",
    "    di = deepcopy(di0)\n",
    "    function pi(μ)\n",
    "        return ψ*μ/(ψ*μ + (1.0 - ψ)*(1.0 - μ))\n",
    "    end\n",
    "    ## compute the trading gain intensities    \n",
    "    di[:ABar] = n*di[:mDO]/md*(1.0 - pi(di[:mDO]/md))^(n-1)/(1.0 - (1.0 - pi(di[:mDO]/md))^n)\n",
    "    di[:BBar] = n*di[:mDN]/md*(1.0 - pi(di[:mDN]/md))^(n-1)/(1.0 - (1.0 - pi(di[:mDN]/md))^n)\n",
    "    di[:ζLO] = di[:vlm]/di[:mLO]*(qLO + (1.0 - qLO)*(1.0 - di[:BBar]))\n",
    "    di[:ζHN] = di[:vlm]/di[:mHN]*(qHN + (1.0 - qHN)*(1.0 - di[:ABar]))\n",
    "    di[:ζDO] = di[:vlm]/di[:mDO]*(1.0 - qHN)*di[:ABar]\n",
    "    di[:ζDN] = di[:vlm]/di[:mDN]*(1.0 - qLO)*di[:BBar]\n",
    "    ## compute value functions, trading gains, and reservation values\n",
    "    ΔDenominator = r^2 + di[:ζDO]*di[:ζLO] + di[:ζLO]*(di[:ζHN] + λd) + di[:ζHN]*λu + di[:ζDO]*(λd + λu) + di[:ζDN]*(di[:ζHN] + λd + λu) + r*(di[:ζDN] + di[:ζDO] + di[:ζHN] + di[:ζLO] + λd + λu)\n",
    "    vDenominator = r*(r + λd + λu)\n",
    "    di[:ΔHD] = maximum([0.0, (yl*(λd - di[:ζDN]) - yd*(r + λd + λu + di[:ζLO]) + yh*(r + λu + di[:ζDN] + di[:ζLO]))/ΔDenominator])\n",
    "    di[:ΔDL] = maximum([0.0, (-yl*(r + λd + di[:ζDO] + di[:ζHN]) + yd*(r + λd + λu + di[:ζHN]) + yh*(di[:ζDO] - λu))/ΔDenominator])\n",
    "    di[:Rd]  = (yd + di[:ζDO]*di[:ΔHD] - di[:ζDN]*di[:ΔDL])/r\n",
    "    di[:Rl]  = ((r + λd)*yl + λu*yh + (r + λd)*di[:ζLO]*di[:ΔDL] - λu*di[:ζHN]*di[:ΔHD])/vDenominator\n",
    "    di[:Rh]  = (λd*yl + (r + λu)*yh + λd*di[:ζLO]*di[:ΔDL] - (r + λu)*di[:ζHN]*di[:ΔHD])/vDenominator\n",
    "    di[:vHO] = ((yl + di[:ΔDL]*di[:ζLO])*λd + yh*(r + λu))/vDenominator\n",
    "    di[:vLN] = di[:ΔHD]*di[:ζHN]*λu/vDenominator\n",
    "    di[:vHN] = di[:ΔHD]*di[:ζHN]*(r + λu)/vDenominator\n",
    "    di[:vLO] = ((yl + di[:ΔDL]*di[:ζLO])*(r + λd) + yh*λu)/vDenominator\n",
    "    di[:vDO] = (yd + di[:ΔHD]*di[:ζDO])/r\n",
    "    di[:vDN] = di[:ΔDL]*di[:ζDN]/r\n",
    "    ## welfare\n",
    "    di[:welfare] = (yh*di[:mHO] + yd*di[:mDO] + yl*di[:mLO])/r\n",
    "    ## check if there is positive trading gain\n",
    "    di[:inbound] = (di[:Rh] <= di[:Rd]) - (di[:Rl] >= di[:Rd])\n",
    "    ## return\n",
    "    return di\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Figure 3: Effects of transparency, ψ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 600x600 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 600x600 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject Text(0.7, 0.04, '\\\\shortstack[r]{Transparency, $\\\\psi$}')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### calculate equilibrium\n",
    "\n",
    "## define parameters\n",
    "#          ρ,  n,   λu,   λd,  yh,  yd,  yl,    r, qLO, qHN,  md,    s,   ψ\n",
    "para0 = [1e0, 27, 0.04, 0.31, 1.0, 0.9, 0.0, 0.05, 0.0, 0.0, 0.1, 0.12, 0.5] # ***\n",
    "ρ0, n0, λu, λd, yh, yd, yl, r, qLO, qHN, md, s = para0\n",
    "\n",
    "## range of ψ\n",
    "xRange = range(0.5,1.0,length=100) \n",
    "\n",
    "## variables of interest\n",
    "liVrb = [:welfare, :νLO, :νHN,]\n",
    "\n",
    "## initialize storage\n",
    "diOut = Dict()\n",
    "for pr in liVrb\n",
    "    diOut[pr] = Array{Float64}(undef, length(xRange))\n",
    "end\n",
    "\n",
    "## compute\n",
    "guess = [0.0084,0.0283,0.0256,]\n",
    "for (cc,ψ) in enumerate(xRange)\n",
    "    para = copy(para0)\n",
    "    para[end] = ψ\n",
    "    cvg0, di0 = solveDemographics(para,guess=guess)\n",
    "    di = solveValueFunctions(para,di0)\n",
    "    for pr in liVrb\n",
    "        if cvg0\n",
    "            diOut[pr][cc] = di[pr]\n",
    "        else\n",
    "            diOut[pr][cc] = NaN\n",
    "            guess = [di0[:mDO], di0[:mHN], di0[:mLO]]\n",
    "        end\n",
    "    end\n",
    "end\n",
    "\n",
    "## Figure 3(a): welfare\n",
    "fig = PyPlot.figure(figsize=(5,5), facecolor=\"w\", dpi=120) # create figure\n",
    "fig.subplots_adjust(left=.15, right=.95, bottom=0.10, top=.95) # reduce white spaces\n",
    "ax = fig.add_subplot(111) # create axis for total trading cost\n",
    "ax.plot(xRange, [log(diOut[:welfare][j]/diOut[:welfare][1])*1e4 for j in 1:length(xRange)], ls=\"-\")\n",
    "## set axes ticks and ranges\n",
    "ax.set_xlim([minimum(xRange), maximum(xRange)])\n",
    "ax.set_yticks(0:-10:-40)\n",
    "## format axes\n",
    "ax.spines[\"right\"].set_visible(false)\n",
    "ax.spines[\"top\"].set_visible(false)\n",
    "arrowed_spines(ax) # add arrows\n",
    "## label axis next to arrows\n",
    "ax.annotate(L\"\\shortstack[l]{Welfare loss (relative to $\\psi=0.5$, basis points)}\", xy=(0.03,1.0,), xycoords=\"axes fraction\") # left y label\n",
    "ax.annotate(L\"\\shortstack[r]{Transparency, $\\psi$}\", xy=(0.7,0.04), xycoords=\"axes fraction\") # x-axis label\n",
    "\n",
    "## Figure 3(b): matching rates\n",
    "fig = PyPlot.figure(figsize=(5,5), facecolor=\"w\", dpi=120) # create figure\n",
    "fig.subplots_adjust(left=.15, right=.95, bottom=0.10, top=.95) # reduce white spaces\n",
    "ax = fig.add_subplot(111) # create axis for total trading cost\n",
    "ax.plot(xRange, [diOut[:νLO][j]*1e2 for j in 1:length(xRange)], ls=\"-\", label=L\"$\\nu_{lo}$\")\n",
    "ax.plot(xRange, [diOut[:νHN][j]*1e2 for j in 1:length(xRange)], ls=\"--\", label=L\"$\\nu_{hn}$\")\n",
    "## set axes ticks and ranges\n",
    "ax.set_xlim([minimum(xRange), maximum(xRange)])\n",
    "## format axes\n",
    "ax.spines[\"right\"].set_visible(false)\n",
    "ax.spines[\"top\"].set_visible(false)\n",
    "arrowed_spines(ax) # add arrows\n",
    "## label axis next to arrows\n",
    "ax.annotate(L\"\\shortstack[l]{$\\nu_{lo}$ (solid) and $\\nu_{hn}$ (dashed), \\%}\", xy=(0.03,1.0,), xycoords=\"axes fraction\") # left y label\n",
    "ax.annotate(L\"\\shortstack[r]{Transparency, $\\psi$}\", xy=(0.7,0.04), xycoords=\"axes fraction\") # x-axis label"
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